Make sure you have the latest wireless driver from the laptop manufacturer's web site.

Disable encryption (set it to 'none' or 'off' or similar) and MAC Address filtering on the router and try to connect. If successful you can probably re-enable encryption and reconnect. If not successful ...

Please attach a screen shot of the Networks page (don't collapse the Radar, Connection or Signal History) of the Xirrus Wi-Fi Inspector. If you need help with that see TSG Posting a Screenshot. FWIW to take screen shots with Windows 7 or Vista I prefer to use the built-in Snipping Tool.

There's close to zero chance of interference from those other networks, but you could use channel 11 to make sure of none.

If you have a firewall or security suite with different settings for wired and wireless there is a possibility that it is blocking.

Otherwise, the wireless adapter seems to be defective. If you can reach it through a small cover on the laptop's bottom remove and carefully and firmly replace it several times to cure any possible looseness or corrosion on the contacts.

Before or after you could not connect at home? If only before, then it is meaningless--the adapter could have failed during the trip home. But if that connection was after the home network trouble began ...

I think that they owe you a router replacement or help with this problem. Tell them you just tested and can connect elsewhere and be ready to summarize all the things you've already tried to fix the issue.

I should have suggested that additional test before I said that the adapter appears to be defective.

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